Integrating the Dirichlet-multinomial and multinomial logit models of brand choice

This paper discusses the interpretative benefits that arise from merging the Dirichlet-multinomial (DM) model as a loyalty variable in the multinomial logit (MNL) model of brand choice. The estimated parameters of this hybrid model compare favorably to those of a pure DM model (with no marketing mix variables) as well as those of a standard MNL model with an exponentially smoothed loyalty measure. The hybrid model offers an index of consumer heterogeneity and estimates of each brand's preference share, adjusted for the effects of price and promotional activities. We illustrate the unique interpretations offered by these parameters across four different product categories, showing how changes in heterogeneity (across categories or model specifications) are closely related to changes in the overall impact of marketing mix variables.The author is grateful to Bruce Hardie, Barbara Kahn, Jim Lattin, Len Lodish, Bob Meyer, and Don Morrison for their comments and suggestions. He appreciates the support of Doug Honnold and Information Resources, Inc., for providing the data and computational facilities used in this paper.